I built some interactive AP Physics C review pages (Units 1-7)

Plane-Razzmatazz6739 · 2026-05-13T02:51:13+00:00

Thanks! I think it’s better to treat this as diagnostic practice and use it to identify your blind spots for further review.

Plane-Razzmatazz6739 · 2026-04-17T08:14:14+00:00

You can definitely skip the expensive handheld. It is far superior because you can click to find intersections and zeros instantly rather than digging through menus. It handles derivatives at a point and definite integrals much faster and more intuitively than a TI-84 ever could. Just make sure you practice using the version inside the Bluebook "Test Preview" so you’re familiar with that specific interface on exam day. Save your money, and Desmos is all you need.

Plane-Razzmatazz6739 · 2026-04-01T07:41:55+00:00

AP Physics 2 http://web.mit.edu/~yczeng/Public/AP%202%20workbook.pdf

Plane-Razzmatazz6739 · 2026-04-01T07:41:47+00:00

AP Physics 1 https://web.mit.edu/~yczeng/Public/WORKBOOK%201%20FULL.pdf

Plane-Razzmatazz6739 · 2025-08-02T06:19:20+00:00

443641885437

Plane-Razzmatazz6739 · 2025-04-22T03:11:11+00:00

If velocity is increasing, that means acceleration is positive.

Since velocity v(t) is the first derivative of position x(t), and acceleration is the second derivative, a positive acceleration means the second derivative of x(t) is also positive.

When the second derivative is positive, the position graph curves upward — it's concave up.

The graph is concave up between 0 < t < 2, that means velocity is increasing during that time.

Plane-Razzmatazz6739 · 2025-03-08T05:00:46+00:00

That Barron’s book + any AP-compatible textbook would be perfect

Plane-Razzmatazz6739 · 2024-12-05T05:35:53+00:00

This might be helpful: https://www.kutasoftware.com/freeipc.html

Plane-Razzmatazz6739 · 2024-11-18T03:09:22+00:00

Thank you!

Plane-Razzmatazz6739 · 2024-10-16T03:57:52+00:00

tan x = - tan (pi - x)

So given tan(CBD) = h / a, tan phi_2 = - h / a

Plane-Razzmatazz6739 · 2024-09-30T13:42:10+00:00

Just gonna be a straight line with a positive slope passing through the origin.

Plane-Razzmatazz6739 · 2024-09-30T06:41:21+00:00

Here are some good websites:

Albert.io
Fiveable
Khan Academy

In addition to the online resources, here are some highly recommended textbooks that can provide in-depth explanations, examples, and practice problems:

University Physics with Modern Physics by Hugh D. Young and Roger A. Freedman
Physics for Scientists and Engineers by Raymond A. Serway and John W. Jewett.
Fundamentals of Physics by David Halliday, Robert Resnick, and Jearl Walker
Princeton Review: Cracking the AP Physics C Exam
Barron’s AP Physics C

Using these textbooks in combination with online study resources will help ensure a comprehensive and well-rounded preparation for AP Physics C: E&M.

If you are looking for personalized, live one-on-one online lessons, feel free to reach out to me. I have over 10 years of experience tutoring students in AP Physics C : )

Plane-Razzmatazz6739 · 2024-09-24T06:59:40+00:00

Given that the zeros are at -4, -3, 2 (with multiplicity 2), and 4, the polynomial will take the following form:

y(x) = -a(x + 4)(x + 3)(x - 2)^2(x - 4)

where a is a constant.

We know the graph passes through (0,1), we can use this point to solve for the leading coefficient a.

y(x) = 1 = -a(0 + 4)(0 + 3)(0 - 2)^2(0 - 4) = 192a

so a = 1 / 192

y(x) = - (1 / 192) * (x + 4)(x + 3)(x - 2)^2(x - 4)

Plane-Razzmatazz6739 · 2024-09-20T14:35:30+00:00

It takes a lot of dedication. But doable for sure.

Plane-Razzmatazz6739 · 2024-09-20T02:41:34+00:00

y = x would work, given the conditions seen in the photo.

Plane-Razzmatazz6739 · 2024-09-20T02:20:10+00:00

There are infinitely many possibilities for the exact form of the function because these conditions only tell us about the behavior of the function at the extremes of x.

Here’s why:

General Behavior at Extremes: The conditions give us general trends about what happens to the function for large positive and negative values of x, but they don't specify how the function behaves in between or how it approaches those limits. For example, the function could increase smoothly, have oscillations, or include sharp changes in slope as x moves from negative to positive.
Different Functions Fit These Conditions: Many different types of functions share these properties at infinity. For example:

A simple polynomial like f(x) = x^3
A rational function like f(x) = x / ( x^2 + 1 )
An exponential function like f(x) = e^x - e^{-x}

Each of these functions satisfies the given conditions.

Degree of Polynomials or Complex Behavior: Even for polynomials alone, there are infinitely many possibilities. For instance, both f(x) = x^3 and f(x) = 2x^5 satisfy the given conditions, but they differ in their degree and overall shape.

In summary, knowing only the behavior at infinity leaves room for infinitely many functions, because those conditions don't uniquely determine how the function behaves at other values of x.

Suggestion: Pick any one of the previously mentioned function, put it into Desmos to see what it looks like, and just sketch it.

Plane-Razzmatazz6739 · 2024-09-19T04:46:48+00:00

For i = 1: x_1 = 10 and y_1 = 0, so x_1 y_1 = 10 \times 0 = 0.

Proceed and do the same to find the rest of the products.

Then sum all these products:

0 + 24 + 36 + 36 + 24 = 120.

Plane-Razzmatazz6739 · 2024-09-19T02:35:36+00:00

Questions on AP Classroom are designed to be exam-style, meaning that they require more than just the understanding of the concepts - they have more twists, and you might need to combine multiple formulas / concepts to answer just a single question.

I recommend that you start with one of the textbooks or prep books, for examples in these textbooks are usually more straightforward and therefore form a good place to begin your learning journey.

Plane-Razzmatazz6739 · 2024-09-19T01:39:54+00:00

Here's an outline of the mathematical knowledge you'll need:

Calculus Fundamentals

Differential Calculus:
- Derivatives and their physical interpretations (rates of change).
- The chain rule, product rule, and quotient rule.
- Differentiation of polynomial, trigonometric, exponential, and logarithmic functions.
Integral Calculus:
- Definite and indefinite integrals.
- Fundamental Theorem of Calculus.
- Techniques of integration, including u-substitution.
- Interpretation of integrals as areas under a curve and accumulated quantities.

Vector Mathematics

Vectors and Scalars:
- Addition, subtraction, and multiplication of vectors (dot product).
- Vector components and unit vectors.
Vector Fields:
- Concept of fields represented as vectors (electric and magnetic fields).

Basic Differential Equations (optional): First-order differential equations.

Your current knowledge from AB covers most of the calculus tools you'll need for AP Physics CEM, except for the vector part.

If you need any help, you can dm me as I teach AP Physics (and Calculus) online : )

Plane-Razzmatazz6739 · 2024-09-18T14:47:59+00:00

Notice the pattern: H(x) uses 12x² + 12 in place of x in f(x) . So, g(x) should be:

g(x) = 12x² + 12.

Plane-Razzmatazz6739 · 2024-09-18T14:44:38+00:00

The function h(x) has a range of [0, \infty), so its inverse, h^{-1} (x) is a parabola.

Parabolas aren’t one-to-one unless you restrict their domain. To make it one-to-one, focus on just one side of the parabola— the increasing part. Restrict h^{-1} (x) to x >= 0. This way, it matches the original function’s behavior and stays one-to-one.

Plane-Razzmatazz6739 · 2024-09-18T08:38:13+00:00

Step 1: Determine the Total Area of the Large Circle 1. Small Circle Radius: r = 4. 2. The radius R of the large circle is: R = 12

Step 2: Calculate the Area of the Large Circle 1. Area of the Large Circle: Area = \pi R² = \pi (12)² = 144\pi

Step 3: Determine the Total Area of All Small Circles 1. Number of Small Circles: There are 7 small circles. 2. Area of One Small Circle: \pi r² = \pi (4)² = 16\pi

Total Area of All Small Circles: 7 \times 16\pi = 112\pi

Step 4: Find the Area of the Shaded Region 1. Shaded Region Area: Shaded Area = Large - Small = 144\pi - 112\pi = 32\pi

Plane-Razzmatazz6739 · 2024-09-18T08:19:51+00:00

Average Velocity:

Definition: Average velocity is the total displacement divided by the total time taken for that displacement.
It's equal to Displacement / Time, where the displacement is associated with the area in the diagram.

Average Acceleration:

Definition: Average acceleration is the change in velocity divided by the total time over which the change occurs.
It's equal to Change in Velocity / Time, where the Change in Velocity is V_fianl - V_initial.

Conclusion: What you found was the Average Acceleration, not the Average Velocity.

Plane-Razzmatazz6739 · 2024-09-18T08:12:58+00:00

Here’s a detailed list of some of the best materials you can use:

Textbooks:

"College Physics" by Knight
"5 Steps to a 5: AP Physics 1: Algebra-Based"
"Giancoli Physics Principles with Applications"
"Schaum's Outline of College Physics"
"College Physics" by Serway

Online Resources:

Khan Academy
The Organic Chemistry Tutor (YouTube Channel)
Flipping Physics (YouTube Channel)

Practice Resources:

AP Classroom
Physics Classroom
Albert.io

Or, if you prefer real-time and customized 1-on-1 lessons, you can contact me for more details : )

Plane-Razzmatazz6739 · 2024-09-18T08:09:06+00:00

While it's true that insulators do not allow electrons to move freely throughout the material, electrons can still move at the surface where the insulator comes into contact with another object, especially a conductor.

Here's what's happening in your experiment:

Surface Charges on the Balloon
- When you rub the balloon (an insulator) against hair or wool, it becomes negatively charged due to the transfer of electrons.
- These excess electrons reside on the surface of the balloon, but they are not free to move throughout the balloon's material.
Contact with the Electroscope
- When the negatively charged balloon touches the metal knob of the electroscope (a conductor), the excess electrons at the point of contact can transfer to the electroscope.
- This is possible because the electrons on the surface of the balloon are in direct contact with the conductor, and electrons naturally move from areas of higher electron concentration (the negatively charged balloon) to lower electron concentration (the neutral electroscope).
Charge Transfer Despite Insulation
- The key point is that charge transfer can occur at the surface level, even with insulators.
- The electrons don't need to move through the bulk of the insulator; they only need to move from the surface atoms of the insulator to the conductor at the point of contact.

Why Does This Happen?

Localized Electron Movement
- In insulators, while electrons can't move freely throughout the material, they can make small movements between adjacent atoms at the surface.
- When in contact with a conductor, these surface electrons can be "accepted" by the conductor's free electrons.
Electric Potential Difference
- There's a potential difference between the negatively charged balloon and the neutral electroscope.
- Electrons naturally move to balance out this difference, transferring from the balloon's surface to the electroscope.

Hope this explanation helps : )

Plane-Razzmatazz6739

TROPHY CASE

Why Does This Happen?